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Lower bound of the hadwiger number of graphs by their average degree

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Abstract

The aim of this paper is to show that the minimum Hadwiger number of graphs with average degreek isO(k/√logk). Specially, it follows that Hadwiger’s conjecture is true for almost all graphs withn vertices, furthermore ifk is large enough then for almost all graphs withn vertices andnk edges.

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Authors and Affiliations

  1. Mathematical Institute of the Siberian Branch of the, Soviet Academy of Sciences, Novosibirsk-90, 630090, U.S.S.R.

    A. V. Kostochka

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  1. A. V. Kostochka
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Kostochka, A.V. Lower bound of the hadwiger number of graphs by their average degree. Combinatorica 4, 307–316 (1984). https://doi.org/10.1007/BF02579141

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  • DOI: https://doi.org/10.1007/BF02579141

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